Question

A solid cube of copper of edge 10 cm subjected to a hydraulic pressure of 7 x ${10}^6$ pascal. If Bulk modulus of copper is 140 GPa, then contraction in its volume will be:

• A. 5 x ${10}^{-8}$ $m^3$
• B. 4 x ${10}^{-8}$ $m^3$
• C. 2 x ${10}^{-8}$ $m^3$
• D. ${10}^8$ $m^3$

Answer 1

The correct option is A 5 x ${10}^{-8}$ $m^3$

The correct option is A.

Given,

$Edge=10cm,Pressure=7\times {10}^{6}p$

Bulk modulus $=140Gpa$

So,

Bulk modulus is :

$B=\frac{\frac{p}{\Delta v}}{V}$

Where,

$\frac{\Delta v}{V}$ is the Volumetric strain,

$\Delta v$ change in volume,

$V$ is the original volume.

So, the original volume of the cube is:

$\Delta v=\frac{p\beta }{B}$

$=\frac{7\times {10}^6\times (0.1{)}^3}{140\times {10}^9}$

$=5\times {10}^{-8}{m}^3$